斜靠式拱桥侧倾失稳极限承载能力简化计算方法

A simplified calculation method of lateral buckling ultimate bearing capacity for leaning-type arch bridge

以斜靠式拱桥为研究对象,基于Ritz法,首次推导出了拱轴线为抛物线的斜靠式拱桥弹性侧倾失稳临界荷载计算公式,并基于有限元法验证了所提出的斜靠式拱桥发生侧倾失稳时主拱肋与稳定拱肋间横撑切向和径向受力模型的精确性以及所推导的侧倾失稳临界荷载计算公式的正确性。此外为便于估算斜靠式拱桥的侧倾失稳极限承载能力,最先引入了稳定拱肋和横撑影响系数η1、吊杆非保向力和桥面系影响系数η2、几何和材料双重非线性影响系数η3,提出了便于工程实际应用的斜靠式拱桥侧倾失稳极限承载能力的简化计算公式。研究结果表明:(1)稳定拱肋和横撑影响系数的取值范围为1.3～1.5;(2)吊杆非保向力和桥面系影响系数的取值范围为3.3～3.6;(3)几何、材料双重非线性影响系数的取值范围为0.23～0.28;(4)斜靠式拱桥的侧倾失稳极限承载能力一般为单片拱肋弹性承载能力的1～1.5倍。

Based on the Ritz method, the leaning-type arch bridge is studied and the analytical solution for the lateral buckling critical load of the leaning-type arch ribs with the parabolic arch axis is derived for the first time. The accuracy of lateral and radial mechanical models for the transverse brace between the main arch rib and stable arch rib as well as the correctness of the presented analytical solution are verified by FEM results. To readily estimate the lateral buckling ultimate bearing capacity, the influence coefficient η1 of the stable arch ribs and transverse brace, the influence coefficient η2 of non-directional load of hangers and bridge deck, the influence coefficient η3 of geometric and material dual nonlinearity. Furthermore, a simplified calculation method for the lateral buckling ultimate bearing capacity, which can be conveniently applied to practical engineering, is presented. Results show that： （1） The influence coefficient of the stable arch ribs and transverse is about 1.3 - 1.5 ; （2） The influence coefficient of non-directional load of hangers and deck is about 3.3 - 3.6 ; （3） The influence coefficient of geometric and material dual nonlinearity is O. 23 - 0.28 ; （4） The lateral buckling ultimate bearing capacity of leaning-type arch bridge is approximately 1.0 to 1.5 times as large as that elastic bearing capacity of the naked arch.